Double fraction

A double break is in mathematics a term in which a fraction (for example, one fifth) by another fraction divided is. It is possible to write another fraction line instead of the usual symbol for division, in which the numerator and denominator are again fractions. Double fractions can be simplified by expanding with a suitable factor:

${\displaystyle {{\frac {a}{b}} \over {c}}={{\frac {a}{b}}\cdot {b} \over {{c}\cdot {b}}}={\frac {a}{{c}\cdot {b}}}}$

Note: This only applies to , because you must not divide by. ${\displaystyle {b},{c}\neq 0}$ ${\displaystyle 0}$

The following rule is better known and easier to understand: Double fractions are simplified by multiplying the numerator fraction by the reciprocal of the denominator fraction:

${\displaystyle {\frac {\frac {a}{b}}{\frac {c}{d}}}={{\frac {a}{b}}\cdot {\frac {d}{c}}}={{ad} \over {bc}}}$

with . ${\displaystyle b,c,d\neq 0}$

In the first example, a fraction with the denominator 1 is: ${\displaystyle c}$

${\displaystyle {\frac {\frac {a}{b}}{c}}={\frac {\frac {a}{b}}{\frac {c}{1}}}={{\frac {a}{b}}\cdot {\frac {1}{c}}}={{a} \over {bc}}}$